
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
  "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">

<html xmlns="http://www.w3.org/1999/xhtml">
  <head>
    <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
    <title>10.1. itertools — Functions creating iterators for efficient looping &#8212; Python 3.6.3 documentation</title>
    <link rel="stylesheet" href="../_static/pydoctheme.css" type="text/css" />
    <link rel="stylesheet" href="../_static/pygments.css" type="text/css" />
    <script type="text/javascript">
      var DOCUMENTATION_OPTIONS = {
        URL_ROOT:    '../',
        VERSION:     '3.6.3',
        COLLAPSE_INDEX: false,
        FILE_SUFFIX: '.html',
        HAS_SOURCE:  true,
        SOURCELINK_SUFFIX: '.txt'
      };
    </script>
    <script type="text/javascript" src="../_static/jquery.js"></script>
    <script type="text/javascript" src="../_static/underscore.js"></script>
    <script type="text/javascript" src="../_static/doctools.js"></script>
    <script type="text/javascript" src="../_static/sidebar.js"></script>
    <link rel="search" type="application/opensearchdescription+xml"
          title="Search within Python 3.6.3 documentation"
          href="../_static/opensearch.xml"/>
    <link rel="author" title="About these documents" href="../about.html" />
    <link rel="index" title="Index" href="../genindex.html" />
    <link rel="search" title="Search" href="../search.html" />
    <link rel="copyright" title="Copyright" href="../copyright.html" />
    <link rel="next" title="10.2. functools — Higher-order functions and operations on callable objects" href="functools.html" />
    <link rel="prev" title="10. Functional Programming Modules" href="functional.html" />
    <link rel="shortcut icon" type="image/png" href="../_static/py.png" />
    <link rel="canonical" href="https://docs.python.org/3/library/itertools.html" />
    
    <script type="text/javascript" src="../_static/copybutton.js"></script>
    <script type="text/javascript" src="../_static/switchers.js"></script>
    
    
 

  </head>
  <body>  
    <div class="related" role="navigation" aria-label="related navigation">
      <h3>Navigation</h3>
      <ul>
        <li class="right" style="margin-right: 10px">
          <a href="../genindex.html" title="General Index"
             accesskey="I">index</a></li>
        <li class="right" >
          <a href="../py-modindex.html" title="Python Module Index"
             >modules</a> |</li>
        <li class="right" >
          <a href="functools.html" title="10.2. functools — Higher-order functions and operations on callable objects"
             accesskey="N">next</a> |</li>
        <li class="right" >
          <a href="functional.html" title="10. Functional Programming Modules"
             accesskey="P">previous</a> |</li>
        <li><img src="../_static/py.png" alt=""
                 style="vertical-align: middle; margin-top: -1px"/></li>
        <li><a href="https://www.python.org/">Python</a> &#187;</li>
        <li>
          <span class="language_switcher_placeholder">en</span>
          <span class="version_switcher_placeholder">3.6.3</span>
          <a href="../index.html">Documentation </a> &#187;
        </li>

          <li class="nav-item nav-item-1"><a href="index.html" >The Python Standard Library</a> &#187;</li>
          <li class="nav-item nav-item-2"><a href="functional.html" accesskey="U">10. Functional Programming Modules</a> &#187;</li>
    <li class="right">
        

    <div class="inline-search" style="display: none" role="search">
        <form class="inline-search" action="../search.html" method="get">
          <input placeholder="Quick search" type="text" name="q" />
          <input type="submit" value="Go" />
          <input type="hidden" name="check_keywords" value="yes" />
          <input type="hidden" name="area" value="default" />
        </form>
    </div>
    <script type="text/javascript">$('.inline-search').show(0);</script>
         |
    </li>

      </ul>
    </div>    

    <div class="document">
      <div class="documentwrapper">
        <div class="bodywrapper">
          <div class="body" role="main">
            
  <div class="section" id="module-itertools">
<span id="itertools-functions-creating-iterators-for-efficient-looping"></span><h1>10.1. <a class="reference internal" href="#module-itertools" title="itertools: Functions creating iterators for efficient looping."><code class="xref py py-mod docutils literal"><span class="pre">itertools</span></code></a> — Functions creating iterators for efficient looping<a class="headerlink" href="#module-itertools" title="Permalink to this headline">¶</a></h1>
<hr class="docutils" />
<p>This module implements a number of <a class="reference internal" href="../glossary.html#term-iterator"><span class="xref std std-term">iterator</span></a> building blocks inspired
by constructs from APL, Haskell, and SML.  Each has been recast in a form
suitable for Python.</p>
<p>The module standardizes a core set of fast, memory efficient tools that are
useful by themselves or in combination.  Together, they form an “iterator
algebra” making it possible to construct specialized tools succinctly and
efficiently in pure Python.</p>
<p>For instance, SML provides a tabulation tool: <code class="docutils literal"><span class="pre">tabulate(f)</span></code> which produces a
sequence <code class="docutils literal"><span class="pre">f(0),</span> <span class="pre">f(1),</span> <span class="pre">...</span></code>.  The same effect can be achieved in Python
by combining <a class="reference internal" href="functions.html#map" title="map"><code class="xref py py-func docutils literal"><span class="pre">map()</span></code></a> and <a class="reference internal" href="#itertools.count" title="itertools.count"><code class="xref py py-func docutils literal"><span class="pre">count()</span></code></a> to form <code class="docutils literal"><span class="pre">map(f,</span> <span class="pre">count())</span></code>.</p>
<p>These tools and their built-in counterparts also work well with the high-speed
functions in the <a class="reference internal" href="operator.html#module-operator" title="operator: Functions corresponding to the standard operators."><code class="xref py py-mod docutils literal"><span class="pre">operator</span></code></a> module.  For example, the multiplication
operator can be mapped across two vectors to form an efficient dot-product:
<code class="docutils literal"><span class="pre">sum(map(operator.mul,</span> <span class="pre">vector1,</span> <span class="pre">vector2))</span></code>.</p>
<p><strong>Infinite Iterators:</strong></p>
<table border="1" class="docutils">
<colgroup>
<col width="14%" />
<col width="14%" />
<col width="39%" />
<col width="33%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">Iterator</th>
<th class="head">Arguments</th>
<th class="head">Results</th>
<th class="head">Example</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td><a class="reference internal" href="#itertools.count" title="itertools.count"><code class="xref py py-func docutils literal"><span class="pre">count()</span></code></a></td>
<td>start, [step]</td>
<td>start, start+step, start+2*step, …</td>
<td><code class="docutils literal"><span class="pre">count(10)</span> <span class="pre">--&gt;</span> <span class="pre">10</span> <span class="pre">11</span> <span class="pre">12</span> <span class="pre">13</span> <span class="pre">14</span> <span class="pre">...</span></code></td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#itertools.cycle" title="itertools.cycle"><code class="xref py py-func docutils literal"><span class="pre">cycle()</span></code></a></td>
<td>p</td>
<td>p0, p1, … plast, p0, p1, …</td>
<td><code class="docutils literal"><span class="pre">cycle('ABCD')</span> <span class="pre">--&gt;</span> <span class="pre">A</span> <span class="pre">B</span> <span class="pre">C</span> <span class="pre">D</span> <span class="pre">A</span> <span class="pre">B</span> <span class="pre">C</span> <span class="pre">D</span> <span class="pre">...</span></code></td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#itertools.repeat" title="itertools.repeat"><code class="xref py py-func docutils literal"><span class="pre">repeat()</span></code></a></td>
<td>elem [,n]</td>
<td>elem, elem, elem, … endlessly or up to n times</td>
<td><code class="docutils literal"><span class="pre">repeat(10,</span> <span class="pre">3)</span> <span class="pre">--&gt;</span> <span class="pre">10</span> <span class="pre">10</span> <span class="pre">10</span></code></td>
</tr>
</tbody>
</table>
<p><strong>Iterators terminating on the shortest input sequence:</strong></p>
<table border="1" class="docutils">
<colgroup>
<col width="17%" />
<col width="17%" />
<col width="30%" />
<col width="37%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">Iterator</th>
<th class="head">Arguments</th>
<th class="head">Results</th>
<th class="head">Example</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td><a class="reference internal" href="#itertools.accumulate" title="itertools.accumulate"><code class="xref py py-func docutils literal"><span class="pre">accumulate()</span></code></a></td>
<td>p [,func]</td>
<td>p0, p0+p1, p0+p1+p2, …</td>
<td><code class="docutils literal"><span class="pre">accumulate([1,2,3,4,5])</span> <span class="pre">--&gt;</span> <span class="pre">1</span> <span class="pre">3</span> <span class="pre">6</span> <span class="pre">10</span> <span class="pre">15</span></code></td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#itertools.chain" title="itertools.chain"><code class="xref py py-func docutils literal"><span class="pre">chain()</span></code></a></td>
<td>p, q, …</td>
<td>p0, p1, … plast, q0, q1, …</td>
<td><code class="docutils literal"><span class="pre">chain('ABC',</span> <span class="pre">'DEF')</span> <span class="pre">--&gt;</span> <span class="pre">A</span> <span class="pre">B</span> <span class="pre">C</span> <span class="pre">D</span> <span class="pre">E</span> <span class="pre">F</span></code></td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#itertools.chain.from_iterable" title="itertools.chain.from_iterable"><code class="xref py py-func docutils literal"><span class="pre">chain.from_iterable()</span></code></a></td>
<td>iterable</td>
<td>p0, p1, … plast, q0, q1, …</td>
<td><code class="docutils literal"><span class="pre">chain.from_iterable(['ABC',</span> <span class="pre">'DEF'])</span> <span class="pre">--&gt;</span> <span class="pre">A</span> <span class="pre">B</span> <span class="pre">C</span> <span class="pre">D</span> <span class="pre">E</span> <span class="pre">F</span></code></td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#itertools.compress" title="itertools.compress"><code class="xref py py-func docutils literal"><span class="pre">compress()</span></code></a></td>
<td>data, selectors</td>
<td>(d[0] if s[0]), (d[1] if s[1]), …</td>
<td><code class="docutils literal"><span class="pre">compress('ABCDEF',</span> <span class="pre">[1,0,1,0,1,1])</span> <span class="pre">--&gt;</span> <span class="pre">A</span> <span class="pre">C</span> <span class="pre">E</span> <span class="pre">F</span></code></td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#itertools.dropwhile" title="itertools.dropwhile"><code class="xref py py-func docutils literal"><span class="pre">dropwhile()</span></code></a></td>
<td>pred, seq</td>
<td>seq[n], seq[n+1], starting when pred fails</td>
<td><code class="docutils literal"><span class="pre">dropwhile(lambda</span> <span class="pre">x:</span> <span class="pre">x&lt;5,</span> <span class="pre">[1,4,6,4,1])</span> <span class="pre">--&gt;</span> <span class="pre">6</span> <span class="pre">4</span> <span class="pre">1</span></code></td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#itertools.filterfalse" title="itertools.filterfalse"><code class="xref py py-func docutils literal"><span class="pre">filterfalse()</span></code></a></td>
<td>pred, seq</td>
<td>elements of seq where pred(elem) is false</td>
<td><code class="docutils literal"><span class="pre">filterfalse(lambda</span> <span class="pre">x:</span> <span class="pre">x%2,</span> <span class="pre">range(10))</span> <span class="pre">--&gt;</span> <span class="pre">0</span> <span class="pre">2</span> <span class="pre">4</span> <span class="pre">6</span> <span class="pre">8</span></code></td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#itertools.groupby" title="itertools.groupby"><code class="xref py py-func docutils literal"><span class="pre">groupby()</span></code></a></td>
<td>iterable[, key]</td>
<td>sub-iterators grouped by value of key(v)</td>
<td>&#160;</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#itertools.islice" title="itertools.islice"><code class="xref py py-func docutils literal"><span class="pre">islice()</span></code></a></td>
<td>seq, [start,] stop [, step]</td>
<td>elements from seq[start:stop:step]</td>
<td><code class="docutils literal"><span class="pre">islice('ABCDEFG',</span> <span class="pre">2,</span> <span class="pre">None)</span> <span class="pre">--&gt;</span> <span class="pre">C</span> <span class="pre">D</span> <span class="pre">E</span> <span class="pre">F</span> <span class="pre">G</span></code></td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#itertools.starmap" title="itertools.starmap"><code class="xref py py-func docutils literal"><span class="pre">starmap()</span></code></a></td>
<td>func, seq</td>
<td>func(*seq[0]), func(*seq[1]), …</td>
<td><code class="docutils literal"><span class="pre">starmap(pow,</span> <span class="pre">[(2,5),</span> <span class="pre">(3,2),</span> <span class="pre">(10,3)])</span> <span class="pre">--&gt;</span> <span class="pre">32</span> <span class="pre">9</span> <span class="pre">1000</span></code></td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#itertools.takewhile" title="itertools.takewhile"><code class="xref py py-func docutils literal"><span class="pre">takewhile()</span></code></a></td>
<td>pred, seq</td>
<td>seq[0], seq[1], until pred fails</td>
<td><code class="docutils literal"><span class="pre">takewhile(lambda</span> <span class="pre">x:</span> <span class="pre">x&lt;5,</span> <span class="pre">[1,4,6,4,1])</span> <span class="pre">--&gt;</span> <span class="pre">1</span> <span class="pre">4</span></code></td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#itertools.tee" title="itertools.tee"><code class="xref py py-func docutils literal"><span class="pre">tee()</span></code></a></td>
<td>it, n</td>
<td>it1, it2, … itn  splits one iterator into n</td>
<td>&#160;</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#itertools.zip_longest" title="itertools.zip_longest"><code class="xref py py-func docutils literal"><span class="pre">zip_longest()</span></code></a></td>
<td>p, q, …</td>
<td>(p[0], q[0]), (p[1], q[1]), …</td>
<td><code class="docutils literal"><span class="pre">zip_longest('ABCD',</span> <span class="pre">'xy',</span> <span class="pre">fillvalue='-')</span> <span class="pre">--&gt;</span> <span class="pre">Ax</span> <span class="pre">By</span> <span class="pre">C-</span> <span class="pre">D-</span></code></td>
</tr>
</tbody>
</table>
<p><strong>Combinatoric generators:</strong></p>
<table border="1" class="docutils">
<colgroup>
<col width="36%" />
<col width="16%" />
<col width="48%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">Iterator</th>
<th class="head">Arguments</th>
<th class="head">Results</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td><a class="reference internal" href="#itertools.product" title="itertools.product"><code class="xref py py-func docutils literal"><span class="pre">product()</span></code></a></td>
<td>p, q, … [repeat=1]</td>
<td>cartesian product, equivalent to a nested for-loop</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#itertools.permutations" title="itertools.permutations"><code class="xref py py-func docutils literal"><span class="pre">permutations()</span></code></a></td>
<td>p[, r]</td>
<td>r-length tuples, all possible orderings, no repeated elements</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#itertools.combinations" title="itertools.combinations"><code class="xref py py-func docutils literal"><span class="pre">combinations()</span></code></a></td>
<td>p, r</td>
<td>r-length tuples, in sorted order, no repeated elements</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#itertools.combinations_with_replacement" title="itertools.combinations_with_replacement"><code class="xref py py-func docutils literal"><span class="pre">combinations_with_replacement()</span></code></a></td>
<td>p, r</td>
<td>r-length tuples, in sorted order, with repeated elements</td>
</tr>
<tr class="row-even"><td><code class="docutils literal"><span class="pre">product('ABCD',</span> <span class="pre">repeat=2)</span></code></td>
<td>&#160;</td>
<td><code class="docutils literal"><span class="pre">AA</span> <span class="pre">AB</span> <span class="pre">AC</span> <span class="pre">AD</span> <span class="pre">BA</span> <span class="pre">BB</span> <span class="pre">BC</span> <span class="pre">BD</span> <span class="pre">CA</span> <span class="pre">CB</span> <span class="pre">CC</span> <span class="pre">CD</span> <span class="pre">DA</span> <span class="pre">DB</span> <span class="pre">DC</span> <span class="pre">DD</span></code></td>
</tr>
<tr class="row-odd"><td><code class="docutils literal"><span class="pre">permutations('ABCD',</span> <span class="pre">2)</span></code></td>
<td>&#160;</td>
<td><code class="docutils literal"><span class="pre">AB</span> <span class="pre">AC</span> <span class="pre">AD</span> <span class="pre">BA</span> <span class="pre">BC</span> <span class="pre">BD</span> <span class="pre">CA</span> <span class="pre">CB</span> <span class="pre">CD</span> <span class="pre">DA</span> <span class="pre">DB</span> <span class="pre">DC</span></code></td>
</tr>
<tr class="row-even"><td><code class="docutils literal"><span class="pre">combinations('ABCD',</span> <span class="pre">2)</span></code></td>
<td>&#160;</td>
<td><code class="docutils literal"><span class="pre">AB</span> <span class="pre">AC</span> <span class="pre">AD</span> <span class="pre">BC</span> <span class="pre">BD</span> <span class="pre">CD</span></code></td>
</tr>
<tr class="row-odd"><td><code class="docutils literal"><span class="pre">combinations_with_replacement('ABCD',</span> <span class="pre">2)</span></code></td>
<td>&#160;</td>
<td><code class="docutils literal"><span class="pre">AA</span> <span class="pre">AB</span> <span class="pre">AC</span> <span class="pre">AD</span> <span class="pre">BB</span> <span class="pre">BC</span> <span class="pre">BD</span> <span class="pre">CC</span> <span class="pre">CD</span> <span class="pre">DD</span></code></td>
</tr>
</tbody>
</table>
<div class="section" id="itertool-functions">
<span id="itertools-functions"></span><h2>10.1.1. Itertool functions<a class="headerlink" href="#itertool-functions" title="Permalink to this headline">¶</a></h2>
<p>The following module functions all construct and return iterators. Some provide
streams of infinite length, so they should only be accessed by functions or
loops that truncate the stream.</p>
<dl class="function">
<dt id="itertools.accumulate">
<code class="descclassname">itertools.</code><code class="descname">accumulate</code><span class="sig-paren">(</span><em>iterable</em><span class="optional">[</span>, <em>func</em><span class="optional">]</span><span class="sig-paren">)</span><a class="headerlink" href="#itertools.accumulate" title="Permalink to this definition">¶</a></dt>
<dd><p>Make an iterator that returns accumulated sums, or accumulated
results of other binary functions (specified via the optional
<em>func</em> argument).  If <em>func</em> is supplied, it should be a function
of two arguments. Elements of the input <em>iterable</em> may be any type
that can be accepted as arguments to <em>func</em>. (For example, with
the default operation of addition, elements may be any addable
type including <a class="reference internal" href="decimal.html#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal"><span class="pre">Decimal</span></code></a> or
<a class="reference internal" href="fractions.html#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal"><span class="pre">Fraction</span></code></a>.) If the input iterable is empty, the
output iterable will also be empty.</p>
<p>Roughly equivalent to:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">accumulate</span><span class="p">(</span><span class="n">iterable</span><span class="p">,</span> <span class="n">func</span><span class="o">=</span><span class="n">operator</span><span class="o">.</span><span class="n">add</span><span class="p">):</span>
    <span class="s1">&#39;Return running totals&#39;</span>
    <span class="c1"># accumulate([1,2,3,4,5]) --&gt; 1 3 6 10 15</span>
    <span class="c1"># accumulate([1,2,3,4,5], operator.mul) --&gt; 1 2 6 24 120</span>
    <span class="n">it</span> <span class="o">=</span> <span class="nb">iter</span><span class="p">(</span><span class="n">iterable</span><span class="p">)</span>
    <span class="k">try</span><span class="p">:</span>
        <span class="n">total</span> <span class="o">=</span> <span class="nb">next</span><span class="p">(</span><span class="n">it</span><span class="p">)</span>
    <span class="k">except</span> <span class="ne">StopIteration</span><span class="p">:</span>
        <span class="k">return</span>
    <span class="k">yield</span> <span class="n">total</span>
    <span class="k">for</span> <span class="n">element</span> <span class="ow">in</span> <span class="n">it</span><span class="p">:</span>
        <span class="n">total</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="n">total</span><span class="p">,</span> <span class="n">element</span><span class="p">)</span>
        <span class="k">yield</span> <span class="n">total</span>
</pre></div>
</div>
<p>There are a number of uses for the <em>func</em> argument.  It can be set to
<a class="reference internal" href="functions.html#min" title="min"><code class="xref py py-func docutils literal"><span class="pre">min()</span></code></a> for a running minimum, <a class="reference internal" href="functions.html#max" title="max"><code class="xref py py-func docutils literal"><span class="pre">max()</span></code></a> for a running maximum, or
<a class="reference internal" href="operator.html#operator.mul" title="operator.mul"><code class="xref py py-func docutils literal"><span class="pre">operator.mul()</span></code></a> for a running product.  Amortization tables can be
built by accumulating interest and applying payments.  First-order
<a class="reference external" href="https://en.wikipedia.org/wiki/Recurrence_relation">recurrence relations</a>
can be modeled by supplying the initial value in the iterable and using only
the accumulated total in <em>func</em> argument:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">data</span> <span class="o">=</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">9</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">8</span><span class="p">]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">list</span><span class="p">(</span><span class="n">accumulate</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">operator</span><span class="o">.</span><span class="n">mul</span><span class="p">))</span>     <span class="c1"># running product</span>
<span class="go">[3, 12, 72, 144, 144, 1296, 0, 0, 0, 0]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">list</span><span class="p">(</span><span class="n">accumulate</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="nb">max</span><span class="p">))</span>              <span class="c1"># running maximum</span>
<span class="go">[3, 4, 6, 6, 6, 9, 9, 9, 9, 9]</span>

<span class="go"># Amortize a 5% loan of 1000 with 4 annual payments of 90</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">cashflows</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1000</span><span class="p">,</span> <span class="o">-</span><span class="mi">90</span><span class="p">,</span> <span class="o">-</span><span class="mi">90</span><span class="p">,</span> <span class="o">-</span><span class="mi">90</span><span class="p">,</span> <span class="o">-</span><span class="mi">90</span><span class="p">]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">list</span><span class="p">(</span><span class="n">accumulate</span><span class="p">(</span><span class="n">cashflows</span><span class="p">,</span> <span class="k">lambda</span> <span class="n">bal</span><span class="p">,</span> <span class="n">pmt</span><span class="p">:</span> <span class="n">bal</span><span class="o">*</span><span class="mf">1.05</span> <span class="o">+</span> <span class="n">pmt</span><span class="p">))</span>
<span class="go">[1000, 960.0, 918.0, 873.9000000000001, 827.5950000000001]</span>

<span class="go"># Chaotic recurrence relation https://en.wikipedia.org/wiki/Logistic_map</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">logistic_map</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="n">_</span><span class="p">:</span>  <span class="n">r</span> <span class="o">*</span> <span class="n">x</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">x</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">r</span> <span class="o">=</span> <span class="mf">3.8</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">x0</span> <span class="o">=</span> <span class="mf">0.4</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">inputs</span> <span class="o">=</span> <span class="n">repeat</span><span class="p">(</span><span class="n">x0</span><span class="p">,</span> <span class="mi">36</span><span class="p">)</span>     <span class="c1"># only the initial value is used</span>
<span class="gp">&gt;&gt;&gt; </span><span class="p">[</span><span class="nb">format</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="s1">&#39;.2f&#39;</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">accumulate</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">logistic_map</span><span class="p">)]</span>
<span class="go">[&#39;0.40&#39;, &#39;0.91&#39;, &#39;0.30&#39;, &#39;0.81&#39;, &#39;0.60&#39;, &#39;0.92&#39;, &#39;0.29&#39;, &#39;0.79&#39;, &#39;0.63&#39;,</span>
<span class="go"> &#39;0.88&#39;, &#39;0.39&#39;, &#39;0.90&#39;, &#39;0.33&#39;, &#39;0.84&#39;, &#39;0.52&#39;, &#39;0.95&#39;, &#39;0.18&#39;, &#39;0.57&#39;,</span>
<span class="go"> &#39;0.93&#39;, &#39;0.25&#39;, &#39;0.71&#39;, &#39;0.79&#39;, &#39;0.63&#39;, &#39;0.88&#39;, &#39;0.39&#39;, &#39;0.91&#39;, &#39;0.32&#39;,</span>
<span class="go"> &#39;0.83&#39;, &#39;0.54&#39;, &#39;0.95&#39;, &#39;0.20&#39;, &#39;0.60&#39;, &#39;0.91&#39;, &#39;0.30&#39;, &#39;0.80&#39;, &#39;0.60&#39;]</span>
</pre></div>
</div>
<p>See <a class="reference internal" href="functools.html#functools.reduce" title="functools.reduce"><code class="xref py py-func docutils literal"><span class="pre">functools.reduce()</span></code></a> for a similar function that returns only the
final accumulated value.</p>
<div class="versionadded">
<p><span class="versionmodified">New in version 3.2.</span></p>
</div>
<div class="versionchanged">
<p><span class="versionmodified">Changed in version 3.3: </span>Added the optional <em>func</em> parameter.</p>
</div>
</dd></dl>

<dl class="function">
<dt id="itertools.chain">
<code class="descclassname">itertools.</code><code class="descname">chain</code><span class="sig-paren">(</span><em>*iterables</em><span class="sig-paren">)</span><a class="headerlink" href="#itertools.chain" title="Permalink to this definition">¶</a></dt>
<dd><p>Make an iterator that returns elements from the first iterable until it is
exhausted, then proceeds to the next iterable, until all of the iterables are
exhausted.  Used for treating consecutive sequences as a single sequence.
Roughly equivalent to:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">chain</span><span class="p">(</span><span class="o">*</span><span class="n">iterables</span><span class="p">):</span>
    <span class="c1"># chain(&#39;ABC&#39;, &#39;DEF&#39;) --&gt; A B C D E F</span>
    <span class="k">for</span> <span class="n">it</span> <span class="ow">in</span> <span class="n">iterables</span><span class="p">:</span>
        <span class="k">for</span> <span class="n">element</span> <span class="ow">in</span> <span class="n">it</span><span class="p">:</span>
            <span class="k">yield</span> <span class="n">element</span>
</pre></div>
</div>
</dd></dl>

<dl class="classmethod">
<dt id="itertools.chain.from_iterable">
<em class="property">classmethod </em><code class="descclassname">chain.</code><code class="descname">from_iterable</code><span class="sig-paren">(</span><em>iterable</em><span class="sig-paren">)</span><a class="headerlink" href="#itertools.chain.from_iterable" title="Permalink to this definition">¶</a></dt>
<dd><p>Alternate constructor for <a class="reference internal" href="#itertools.chain" title="itertools.chain"><code class="xref py py-func docutils literal"><span class="pre">chain()</span></code></a>.  Gets chained inputs from a
single iterable argument that is evaluated lazily.  Roughly equivalent to:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">from_iterable</span><span class="p">(</span><span class="n">iterables</span><span class="p">):</span>
    <span class="c1"># chain.from_iterable([&#39;ABC&#39;, &#39;DEF&#39;]) --&gt; A B C D E F</span>
    <span class="k">for</span> <span class="n">it</span> <span class="ow">in</span> <span class="n">iterables</span><span class="p">:</span>
        <span class="k">for</span> <span class="n">element</span> <span class="ow">in</span> <span class="n">it</span><span class="p">:</span>
            <span class="k">yield</span> <span class="n">element</span>
</pre></div>
</div>
</dd></dl>

<dl class="function">
<dt id="itertools.combinations">
<code class="descclassname">itertools.</code><code class="descname">combinations</code><span class="sig-paren">(</span><em>iterable</em>, <em>r</em><span class="sig-paren">)</span><a class="headerlink" href="#itertools.combinations" title="Permalink to this definition">¶</a></dt>
<dd><p>Return <em>r</em> length subsequences of elements from the input <em>iterable</em>.</p>
<p>Combinations are emitted in lexicographic sort order.  So, if the
input <em>iterable</em> is sorted, the combination tuples will be produced
in sorted order.</p>
<p>Elements are treated as unique based on their position, not on their
value.  So if the input elements are unique, there will be no repeat
values in each combination.</p>
<p>Roughly equivalent to:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">combinations</span><span class="p">(</span><span class="n">iterable</span><span class="p">,</span> <span class="n">r</span><span class="p">):</span>
    <span class="c1"># combinations(&#39;ABCD&#39;, 2) --&gt; AB AC AD BC BD CD</span>
    <span class="c1"># combinations(range(4), 3) --&gt; 012 013 023 123</span>
    <span class="n">pool</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">iterable</span><span class="p">)</span>
    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">pool</span><span class="p">)</span>
    <span class="k">if</span> <span class="n">r</span> <span class="o">&gt;</span> <span class="n">n</span><span class="p">:</span>
        <span class="k">return</span>
    <span class="n">indices</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">r</span><span class="p">))</span>
    <span class="k">yield</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">pool</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">indices</span><span class="p">)</span>
    <span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">reversed</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">r</span><span class="p">)):</span>
            <span class="k">if</span> <span class="n">indices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">!=</span> <span class="n">i</span> <span class="o">+</span> <span class="n">n</span> <span class="o">-</span> <span class="n">r</span><span class="p">:</span>
                <span class="k">break</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="k">return</span>
        <span class="n">indices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span> <span class="n">r</span><span class="p">):</span>
            <span class="n">indices</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">indices</span><span class="p">[</span><span class="n">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="mi">1</span>
        <span class="k">yield</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">pool</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">indices</span><span class="p">)</span>
</pre></div>
</div>
<p>The code for <a class="reference internal" href="#itertools.combinations" title="itertools.combinations"><code class="xref py py-func docutils literal"><span class="pre">combinations()</span></code></a> can be also expressed as a subsequence
of <a class="reference internal" href="#itertools.permutations" title="itertools.permutations"><code class="xref py py-func docutils literal"><span class="pre">permutations()</span></code></a> after filtering entries where the elements are not
in sorted order (according to their position in the input pool):</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">combinations</span><span class="p">(</span><span class="n">iterable</span><span class="p">,</span> <span class="n">r</span><span class="p">):</span>
    <span class="n">pool</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">iterable</span><span class="p">)</span>
    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">pool</span><span class="p">)</span>
    <span class="k">for</span> <span class="n">indices</span> <span class="ow">in</span> <span class="n">permutations</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">),</span> <span class="n">r</span><span class="p">):</span>
        <span class="k">if</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">indices</span><span class="p">)</span> <span class="o">==</span> <span class="nb">list</span><span class="p">(</span><span class="n">indices</span><span class="p">):</span>
            <span class="k">yield</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">pool</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">indices</span><span class="p">)</span>
</pre></div>
</div>
<p>The number of items returned is <code class="docutils literal"><span class="pre">n!</span> <span class="pre">/</span> <span class="pre">r!</span> <span class="pre">/</span> <span class="pre">(n-r)!</span></code> when <code class="docutils literal"><span class="pre">0</span> <span class="pre">&lt;=</span> <span class="pre">r</span> <span class="pre">&lt;=</span> <span class="pre">n</span></code>
or zero when <code class="docutils literal"><span class="pre">r</span> <span class="pre">&gt;</span> <span class="pre">n</span></code>.</p>
</dd></dl>

<dl class="function">
<dt id="itertools.combinations_with_replacement">
<code class="descclassname">itertools.</code><code class="descname">combinations_with_replacement</code><span class="sig-paren">(</span><em>iterable</em>, <em>r</em><span class="sig-paren">)</span><a class="headerlink" href="#itertools.combinations_with_replacement" title="Permalink to this definition">¶</a></dt>
<dd><p>Return <em>r</em> length subsequences of elements from the input <em>iterable</em>
allowing individual elements to be repeated more than once.</p>
<p>Combinations are emitted in lexicographic sort order.  So, if the
input <em>iterable</em> is sorted, the combination tuples will be produced
in sorted order.</p>
<p>Elements are treated as unique based on their position, not on their
value.  So if the input elements are unique, the generated combinations
will also be unique.</p>
<p>Roughly equivalent to:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">combinations_with_replacement</span><span class="p">(</span><span class="n">iterable</span><span class="p">,</span> <span class="n">r</span><span class="p">):</span>
    <span class="c1"># combinations_with_replacement(&#39;ABC&#39;, 2) --&gt; AA AB AC BB BC CC</span>
    <span class="n">pool</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">iterable</span><span class="p">)</span>
    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">pool</span><span class="p">)</span>
    <span class="k">if</span> <span class="ow">not</span> <span class="n">n</span> <span class="ow">and</span> <span class="n">r</span><span class="p">:</span>
        <span class="k">return</span>
    <span class="n">indices</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">r</span>
    <span class="k">yield</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">pool</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">indices</span><span class="p">)</span>
    <span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">reversed</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">r</span><span class="p">)):</span>
            <span class="k">if</span> <span class="n">indices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">!=</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">:</span>
                <span class="k">break</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="k">return</span>
        <span class="n">indices</span><span class="p">[</span><span class="n">i</span><span class="p">:]</span> <span class="o">=</span> <span class="p">[</span><span class="n">indices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">r</span> <span class="o">-</span> <span class="n">i</span><span class="p">)</span>
        <span class="k">yield</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">pool</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">indices</span><span class="p">)</span>
</pre></div>
</div>
<p>The code for <a class="reference internal" href="#itertools.combinations_with_replacement" title="itertools.combinations_with_replacement"><code class="xref py py-func docutils literal"><span class="pre">combinations_with_replacement()</span></code></a> can be also expressed as
a subsequence of <a class="reference internal" href="#itertools.product" title="itertools.product"><code class="xref py py-func docutils literal"><span class="pre">product()</span></code></a> after filtering entries where the elements
are not in sorted order (according to their position in the input pool):</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">combinations_with_replacement</span><span class="p">(</span><span class="n">iterable</span><span class="p">,</span> <span class="n">r</span><span class="p">):</span>
    <span class="n">pool</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">iterable</span><span class="p">)</span>
    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">pool</span><span class="p">)</span>
    <span class="k">for</span> <span class="n">indices</span> <span class="ow">in</span> <span class="n">product</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">),</span> <span class="n">repeat</span><span class="o">=</span><span class="n">r</span><span class="p">):</span>
        <span class="k">if</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">indices</span><span class="p">)</span> <span class="o">==</span> <span class="nb">list</span><span class="p">(</span><span class="n">indices</span><span class="p">):</span>
            <span class="k">yield</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">pool</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">indices</span><span class="p">)</span>
</pre></div>
</div>
<p>The number of items returned is <code class="docutils literal"><span class="pre">(n+r-1)!</span> <span class="pre">/</span> <span class="pre">r!</span> <span class="pre">/</span> <span class="pre">(n-1)!</span></code> when <code class="docutils literal"><span class="pre">n</span> <span class="pre">&gt;</span> <span class="pre">0</span></code>.</p>
<div class="versionadded">
<p><span class="versionmodified">New in version 3.1.</span></p>
</div>
</dd></dl>

<dl class="function">
<dt id="itertools.compress">
<code class="descclassname">itertools.</code><code class="descname">compress</code><span class="sig-paren">(</span><em>data</em>, <em>selectors</em><span class="sig-paren">)</span><a class="headerlink" href="#itertools.compress" title="Permalink to this definition">¶</a></dt>
<dd><p>Make an iterator that filters elements from <em>data</em> returning only those that
have a corresponding element in <em>selectors</em> that evaluates to <code class="docutils literal"><span class="pre">True</span></code>.
Stops when either the <em>data</em> or <em>selectors</em> iterables has been exhausted.
Roughly equivalent to:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compress</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">selectors</span><span class="p">):</span>
    <span class="c1"># compress(&#39;ABCDEF&#39;, [1,0,1,0,1,1]) --&gt; A C E F</span>
    <span class="k">return</span> <span class="p">(</span><span class="n">d</span> <span class="k">for</span> <span class="n">d</span><span class="p">,</span> <span class="n">s</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">selectors</span><span class="p">)</span> <span class="k">if</span> <span class="n">s</span><span class="p">)</span>
</pre></div>
</div>
<div class="versionadded">
<p><span class="versionmodified">New in version 3.1.</span></p>
</div>
</dd></dl>

<dl class="function">
<dt id="itertools.count">
<code class="descclassname">itertools.</code><code class="descname">count</code><span class="sig-paren">(</span><em>start=0</em>, <em>step=1</em><span class="sig-paren">)</span><a class="headerlink" href="#itertools.count" title="Permalink to this definition">¶</a></dt>
<dd><p>Make an iterator that returns evenly spaced values starting with number <em>start</em>. Often
used as an argument to <a class="reference internal" href="functions.html#map" title="map"><code class="xref py py-func docutils literal"><span class="pre">map()</span></code></a> to generate consecutive data points.
Also, used with <a class="reference internal" href="functions.html#zip" title="zip"><code class="xref py py-func docutils literal"><span class="pre">zip()</span></code></a> to add sequence numbers.  Roughly equivalent to:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">count</span><span class="p">(</span><span class="n">start</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">step</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
    <span class="c1"># count(10) --&gt; 10 11 12 13 14 ...</span>
    <span class="c1"># count(2.5, 0.5) -&gt; 2.5 3.0 3.5 ...</span>
    <span class="n">n</span> <span class="o">=</span> <span class="n">start</span>
    <span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
        <span class="k">yield</span> <span class="n">n</span>
        <span class="n">n</span> <span class="o">+=</span> <span class="n">step</span>
</pre></div>
</div>
<p>When counting with floating point numbers, better accuracy can sometimes be
achieved by substituting multiplicative code such as: <code class="docutils literal"><span class="pre">(start</span> <span class="pre">+</span> <span class="pre">step</span> <span class="pre">*</span> <span class="pre">i</span>
<span class="pre">for</span> <span class="pre">i</span> <span class="pre">in</span> <span class="pre">count())</span></code>.</p>
<div class="versionchanged">
<p><span class="versionmodified">Changed in version 3.1: </span>Added <em>step</em> argument and allowed non-integer arguments.</p>
</div>
</dd></dl>

<dl class="function">
<dt id="itertools.cycle">
<code class="descclassname">itertools.</code><code class="descname">cycle</code><span class="sig-paren">(</span><em>iterable</em><span class="sig-paren">)</span><a class="headerlink" href="#itertools.cycle" title="Permalink to this definition">¶</a></dt>
<dd><p>Make an iterator returning elements from the iterable and saving a copy of each.
When the iterable is exhausted, return elements from the saved copy.  Repeats
indefinitely.  Roughly equivalent to:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">cycle</span><span class="p">(</span><span class="n">iterable</span><span class="p">):</span>
    <span class="c1"># cycle(&#39;ABCD&#39;) --&gt; A B C D A B C D A B C D ...</span>
    <span class="n">saved</span> <span class="o">=</span> <span class="p">[]</span>
    <span class="k">for</span> <span class="n">element</span> <span class="ow">in</span> <span class="n">iterable</span><span class="p">:</span>
        <span class="k">yield</span> <span class="n">element</span>
        <span class="n">saved</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">element</span><span class="p">)</span>
    <span class="k">while</span> <span class="n">saved</span><span class="p">:</span>
        <span class="k">for</span> <span class="n">element</span> <span class="ow">in</span> <span class="n">saved</span><span class="p">:</span>
              <span class="k">yield</span> <span class="n">element</span>
</pre></div>
</div>
<p>Note, this member of the toolkit may require significant auxiliary storage
(depending on the length of the iterable).</p>
</dd></dl>

<dl class="function">
<dt id="itertools.dropwhile">
<code class="descclassname">itertools.</code><code class="descname">dropwhile</code><span class="sig-paren">(</span><em>predicate</em>, <em>iterable</em><span class="sig-paren">)</span><a class="headerlink" href="#itertools.dropwhile" title="Permalink to this definition">¶</a></dt>
<dd><p>Make an iterator that drops elements from the iterable as long as the predicate
is true; afterwards, returns every element.  Note, the iterator does not produce
<em>any</em> output until the predicate first becomes false, so it may have a lengthy
start-up time.  Roughly equivalent to:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">dropwhile</span><span class="p">(</span><span class="n">predicate</span><span class="p">,</span> <span class="n">iterable</span><span class="p">):</span>
    <span class="c1"># dropwhile(lambda x: x&lt;5, [1,4,6,4,1]) --&gt; 6 4 1</span>
    <span class="n">iterable</span> <span class="o">=</span> <span class="nb">iter</span><span class="p">(</span><span class="n">iterable</span><span class="p">)</span>
    <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">iterable</span><span class="p">:</span>
        <span class="k">if</span> <span class="ow">not</span> <span class="n">predicate</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
            <span class="k">yield</span> <span class="n">x</span>
            <span class="k">break</span>
    <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">iterable</span><span class="p">:</span>
        <span class="k">yield</span> <span class="n">x</span>
</pre></div>
</div>
</dd></dl>

<dl class="function">
<dt id="itertools.filterfalse">
<code class="descclassname">itertools.</code><code class="descname">filterfalse</code><span class="sig-paren">(</span><em>predicate</em>, <em>iterable</em><span class="sig-paren">)</span><a class="headerlink" href="#itertools.filterfalse" title="Permalink to this definition">¶</a></dt>
<dd><p>Make an iterator that filters elements from iterable returning only those for
which the predicate is <code class="docutils literal"><span class="pre">False</span></code>. If <em>predicate</em> is <code class="docutils literal"><span class="pre">None</span></code>, return the items
that are false. Roughly equivalent to:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">filterfalse</span><span class="p">(</span><span class="n">predicate</span><span class="p">,</span> <span class="n">iterable</span><span class="p">):</span>
    <span class="c1"># filterfalse(lambda x: x%2, range(10)) --&gt; 0 2 4 6 8</span>
    <span class="k">if</span> <span class="n">predicate</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
        <span class="n">predicate</span> <span class="o">=</span> <span class="nb">bool</span>
    <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">iterable</span><span class="p">:</span>
        <span class="k">if</span> <span class="ow">not</span> <span class="n">predicate</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
            <span class="k">yield</span> <span class="n">x</span>
</pre></div>
</div>
</dd></dl>

<dl class="function">
<dt id="itertools.groupby">
<code class="descclassname">itertools.</code><code class="descname">groupby</code><span class="sig-paren">(</span><em>iterable</em>, <em>key=None</em><span class="sig-paren">)</span><a class="headerlink" href="#itertools.groupby" title="Permalink to this definition">¶</a></dt>
<dd><p>Make an iterator that returns consecutive keys and groups from the <em>iterable</em>.
The <em>key</em> is a function computing a key value for each element.  If not
specified or is <code class="docutils literal"><span class="pre">None</span></code>, <em>key</em> defaults to an identity function and returns
the element unchanged.  Generally, the iterable needs to already be sorted on
the same key function.</p>
<p>The operation of <a class="reference internal" href="#itertools.groupby" title="itertools.groupby"><code class="xref py py-func docutils literal"><span class="pre">groupby()</span></code></a> is similar to the <code class="docutils literal"><span class="pre">uniq</span></code> filter in Unix.  It
generates a break or new group every time the value of the key function changes
(which is why it is usually necessary to have sorted the data using the same key
function).  That behavior differs from SQL’s GROUP BY which aggregates common
elements regardless of their input order.</p>
<p>The returned group is itself an iterator that shares the underlying iterable
with <a class="reference internal" href="#itertools.groupby" title="itertools.groupby"><code class="xref py py-func docutils literal"><span class="pre">groupby()</span></code></a>.  Because the source is shared, when the <a class="reference internal" href="#itertools.groupby" title="itertools.groupby"><code class="xref py py-func docutils literal"><span class="pre">groupby()</span></code></a>
object is advanced, the previous group is no longer visible.  So, if that data
is needed later, it should be stored as a list:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="n">groups</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">uniquekeys</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">data</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">key</span><span class="o">=</span><span class="n">keyfunc</span><span class="p">)</span>
<span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">g</span> <span class="ow">in</span> <span class="n">groupby</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">keyfunc</span><span class="p">):</span>
    <span class="n">groups</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">g</span><span class="p">))</span>      <span class="c1"># Store group iterator as a list</span>
    <span class="n">uniquekeys</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">k</span><span class="p">)</span>
</pre></div>
</div>
<p><a class="reference internal" href="#itertools.groupby" title="itertools.groupby"><code class="xref py py-func docutils literal"><span class="pre">groupby()</span></code></a> is roughly equivalent to:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">groupby</span><span class="p">:</span>
    <span class="c1"># [k for k, g in groupby(&#39;AAAABBBCCDAABBB&#39;)] --&gt; A B C D A B</span>
    <span class="c1"># [list(g) for k, g in groupby(&#39;AAAABBBCCD&#39;)] --&gt; AAAA BBB CC D</span>
    <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">iterable</span><span class="p">,</span> <span class="n">key</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
        <span class="k">if</span> <span class="n">key</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
            <span class="n">key</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">x</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">keyfunc</span> <span class="o">=</span> <span class="n">key</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">it</span> <span class="o">=</span> <span class="nb">iter</span><span class="p">(</span><span class="n">iterable</span><span class="p">)</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">tgtkey</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">currkey</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">currvalue</span> <span class="o">=</span> <span class="nb">object</span><span class="p">()</span>
    <span class="k">def</span> <span class="nf">__iter__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="k">return</span> <span class="bp">self</span>
    <span class="k">def</span> <span class="nf">__next__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="k">while</span> <span class="bp">self</span><span class="o">.</span><span class="n">currkey</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">tgtkey</span><span class="p">:</span>
            <span class="bp">self</span><span class="o">.</span><span class="n">currvalue</span> <span class="o">=</span> <span class="nb">next</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">it</span><span class="p">)</span>    <span class="c1"># Exit on StopIteration</span>
            <span class="bp">self</span><span class="o">.</span><span class="n">currkey</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">keyfunc</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">currvalue</span><span class="p">)</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">tgtkey</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">currkey</span>
        <span class="k">return</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">currkey</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">_grouper</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">tgtkey</span><span class="p">))</span>
    <span class="k">def</span> <span class="nf">_grouper</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">tgtkey</span><span class="p">):</span>
        <span class="k">while</span> <span class="bp">self</span><span class="o">.</span><span class="n">currkey</span> <span class="o">==</span> <span class="n">tgtkey</span><span class="p">:</span>
            <span class="k">yield</span> <span class="bp">self</span><span class="o">.</span><span class="n">currvalue</span>
            <span class="k">try</span><span class="p">:</span>
                <span class="bp">self</span><span class="o">.</span><span class="n">currvalue</span> <span class="o">=</span> <span class="nb">next</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">it</span><span class="p">)</span>
            <span class="k">except</span> <span class="ne">StopIteration</span><span class="p">:</span>
                <span class="k">return</span>
            <span class="bp">self</span><span class="o">.</span><span class="n">currkey</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">keyfunc</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">currvalue</span><span class="p">)</span>
</pre></div>
</div>
</dd></dl>

<dl class="function">
<dt id="itertools.islice">
<code class="descclassname">itertools.</code><code class="descname">islice</code><span class="sig-paren">(</span><em>iterable</em>, <em>stop</em><span class="sig-paren">)</span><a class="headerlink" href="#itertools.islice" title="Permalink to this definition">¶</a></dt>
<dt>
<code class="descclassname">itertools.</code><code class="descname">islice</code><span class="sig-paren">(</span><em>iterable</em>, <em>start</em>, <em>stop</em><span class="optional">[</span>, <em>step</em><span class="optional">]</span><span class="sig-paren">)</span></dt>
<dd><p>Make an iterator that returns selected elements from the iterable. If <em>start</em> is
non-zero, then elements from the iterable are skipped until start is reached.
Afterward, elements are returned consecutively unless <em>step</em> is set higher than
one which results in items being skipped.  If <em>stop</em> is <code class="docutils literal"><span class="pre">None</span></code>, then iteration
continues until the iterator is exhausted, if at all; otherwise, it stops at the
specified position.  Unlike regular slicing, <a class="reference internal" href="#itertools.islice" title="itertools.islice"><code class="xref py py-func docutils literal"><span class="pre">islice()</span></code></a> does not support
negative values for <em>start</em>, <em>stop</em>, or <em>step</em>.  Can be used to extract related
fields from data where the internal structure has been flattened (for example, a
multi-line report may list a name field on every third line).  Roughly equivalent to:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">islice</span><span class="p">(</span><span class="n">iterable</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">):</span>
    <span class="c1"># islice(&#39;ABCDEFG&#39;, 2) --&gt; A B</span>
    <span class="c1"># islice(&#39;ABCDEFG&#39;, 2, 4) --&gt; C D</span>
    <span class="c1"># islice(&#39;ABCDEFG&#39;, 2, None) --&gt; C D E F G</span>
    <span class="c1"># islice(&#39;ABCDEFG&#39;, 0, None, 2) --&gt; A C E G</span>
    <span class="n">s</span> <span class="o">=</span> <span class="nb">slice</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">)</span>
    <span class="n">it</span> <span class="o">=</span> <span class="nb">iter</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">s</span><span class="o">.</span><span class="n">start</span> <span class="ow">or</span> <span class="mi">0</span><span class="p">,</span> <span class="n">s</span><span class="o">.</span><span class="n">stop</span> <span class="ow">or</span> <span class="n">sys</span><span class="o">.</span><span class="n">maxsize</span><span class="p">,</span> <span class="n">s</span><span class="o">.</span><span class="n">step</span> <span class="ow">or</span> <span class="mi">1</span><span class="p">))</span>
    <span class="k">try</span><span class="p">:</span>
        <span class="n">nexti</span> <span class="o">=</span> <span class="nb">next</span><span class="p">(</span><span class="n">it</span><span class="p">)</span>
    <span class="k">except</span> <span class="ne">StopIteration</span><span class="p">:</span>
        <span class="k">return</span>
    <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">element</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">iterable</span><span class="p">):</span>
        <span class="k">if</span> <span class="n">i</span> <span class="o">==</span> <span class="n">nexti</span><span class="p">:</span>
            <span class="k">yield</span> <span class="n">element</span>
            <span class="n">nexti</span> <span class="o">=</span> <span class="nb">next</span><span class="p">(</span><span class="n">it</span><span class="p">)</span>
</pre></div>
</div>
<p>If <em>start</em> is <code class="docutils literal"><span class="pre">None</span></code>, then iteration starts at zero. If <em>step</em> is <code class="docutils literal"><span class="pre">None</span></code>,
then the step defaults to one.</p>
</dd></dl>

<dl class="function">
<dt id="itertools.permutations">
<code class="descclassname">itertools.</code><code class="descname">permutations</code><span class="sig-paren">(</span><em>iterable</em>, <em>r=None</em><span class="sig-paren">)</span><a class="headerlink" href="#itertools.permutations" title="Permalink to this definition">¶</a></dt>
<dd><p>Return successive <em>r</em> length permutations of elements in the <em>iterable</em>.</p>
<p>If <em>r</em> is not specified or is <code class="docutils literal"><span class="pre">None</span></code>, then <em>r</em> defaults to the length
of the <em>iterable</em> and all possible full-length permutations
are generated.</p>
<p>Permutations are emitted in lexicographic sort order.  So, if the
input <em>iterable</em> is sorted, the permutation tuples will be produced
in sorted order.</p>
<p>Elements are treated as unique based on their position, not on their
value.  So if the input elements are unique, there will be no repeat
values in each permutation.</p>
<p>Roughly equivalent to:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">permutations</span><span class="p">(</span><span class="n">iterable</span><span class="p">,</span> <span class="n">r</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
    <span class="c1"># permutations(&#39;ABCD&#39;, 2) --&gt; AB AC AD BA BC BD CA CB CD DA DB DC</span>
    <span class="c1"># permutations(range(3)) --&gt; 012 021 102 120 201 210</span>
    <span class="n">pool</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">iterable</span><span class="p">)</span>
    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">pool</span><span class="p">)</span>
    <span class="n">r</span> <span class="o">=</span> <span class="n">n</span> <span class="k">if</span> <span class="n">r</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="n">r</span>
    <span class="k">if</span> <span class="n">r</span> <span class="o">&gt;</span> <span class="n">n</span><span class="p">:</span>
        <span class="k">return</span>
    <span class="n">indices</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">))</span>
    <span class="n">cycles</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">n</span><span class="o">-</span><span class="n">r</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">))</span>
    <span class="k">yield</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">pool</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">indices</span><span class="p">[:</span><span class="n">r</span><span class="p">])</span>
    <span class="k">while</span> <span class="n">n</span><span class="p">:</span>
        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">reversed</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">r</span><span class="p">)):</span>
            <span class="n">cycles</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">-=</span> <span class="mi">1</span>
            <span class="k">if</span> <span class="n">cycles</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
                <span class="n">indices</span><span class="p">[</span><span class="n">i</span><span class="p">:]</span> <span class="o">=</span> <span class="n">indices</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">:]</span> <span class="o">+</span> <span class="n">indices</span><span class="p">[</span><span class="n">i</span><span class="p">:</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span>
                <span class="n">cycles</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">n</span> <span class="o">-</span> <span class="n">i</span>
            <span class="k">else</span><span class="p">:</span>
                <span class="n">j</span> <span class="o">=</span> <span class="n">cycles</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
                <span class="n">indices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">indices</span><span class="p">[</span><span class="o">-</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">indices</span><span class="p">[</span><span class="o">-</span><span class="n">j</span><span class="p">],</span> <span class="n">indices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
                <span class="k">yield</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">pool</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">indices</span><span class="p">[:</span><span class="n">r</span><span class="p">])</span>
                <span class="k">break</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="k">return</span>
</pre></div>
</div>
<p>The code for <a class="reference internal" href="#itertools.permutations" title="itertools.permutations"><code class="xref py py-func docutils literal"><span class="pre">permutations()</span></code></a> can be also expressed as a subsequence of
<a class="reference internal" href="#itertools.product" title="itertools.product"><code class="xref py py-func docutils literal"><span class="pre">product()</span></code></a>, filtered to exclude entries with repeated elements (those
from the same position in the input pool):</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">permutations</span><span class="p">(</span><span class="n">iterable</span><span class="p">,</span> <span class="n">r</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
    <span class="n">pool</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">iterable</span><span class="p">)</span>
    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">pool</span><span class="p">)</span>
    <span class="n">r</span> <span class="o">=</span> <span class="n">n</span> <span class="k">if</span> <span class="n">r</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="n">r</span>
    <span class="k">for</span> <span class="n">indices</span> <span class="ow">in</span> <span class="n">product</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">),</span> <span class="n">repeat</span><span class="o">=</span><span class="n">r</span><span class="p">):</span>
        <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="nb">set</span><span class="p">(</span><span class="n">indices</span><span class="p">))</span> <span class="o">==</span> <span class="n">r</span><span class="p">:</span>
            <span class="k">yield</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">pool</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">indices</span><span class="p">)</span>
</pre></div>
</div>
<p>The number of items returned is <code class="docutils literal"><span class="pre">n!</span> <span class="pre">/</span> <span class="pre">(n-r)!</span></code> when <code class="docutils literal"><span class="pre">0</span> <span class="pre">&lt;=</span> <span class="pre">r</span> <span class="pre">&lt;=</span> <span class="pre">n</span></code>
or zero when <code class="docutils literal"><span class="pre">r</span> <span class="pre">&gt;</span> <span class="pre">n</span></code>.</p>
</dd></dl>

<dl class="function">
<dt id="itertools.product">
<code class="descclassname">itertools.</code><code class="descname">product</code><span class="sig-paren">(</span><em>*iterables</em>, <em>repeat=1</em><span class="sig-paren">)</span><a class="headerlink" href="#itertools.product" title="Permalink to this definition">¶</a></dt>
<dd><p>Cartesian product of input iterables.</p>
<p>Roughly equivalent to nested for-loops in a generator expression. For example,
<code class="docutils literal"><span class="pre">product(A,</span> <span class="pre">B)</span></code> returns the same as <code class="docutils literal"><span class="pre">((x,y)</span> <span class="pre">for</span> <span class="pre">x</span> <span class="pre">in</span> <span class="pre">A</span> <span class="pre">for</span> <span class="pre">y</span> <span class="pre">in</span> <span class="pre">B)</span></code>.</p>
<p>The nested loops cycle like an odometer with the rightmost element advancing
on every iteration.  This pattern creates a lexicographic ordering so that if
the input’s iterables are sorted, the product tuples are emitted in sorted
order.</p>
<p>To compute the product of an iterable with itself, specify the number of
repetitions with the optional <em>repeat</em> keyword argument.  For example,
<code class="docutils literal"><span class="pre">product(A,</span> <span class="pre">repeat=4)</span></code> means the same as <code class="docutils literal"><span class="pre">product(A,</span> <span class="pre">A,</span> <span class="pre">A,</span> <span class="pre">A)</span></code>.</p>
<p>This function is roughly equivalent to the following code, except that the
actual implementation does not build up intermediate results in memory:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">product</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="n">repeat</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
    <span class="c1"># product(&#39;ABCD&#39;, &#39;xy&#39;) --&gt; Ax Ay Bx By Cx Cy Dx Dy</span>
    <span class="c1"># product(range(2), repeat=3) --&gt; 000 001 010 011 100 101 110 111</span>
    <span class="n">pools</span> <span class="o">=</span> <span class="p">[</span><span class="nb">tuple</span><span class="p">(</span><span class="n">pool</span><span class="p">)</span> <span class="k">for</span> <span class="n">pool</span> <span class="ow">in</span> <span class="n">args</span><span class="p">]</span> <span class="o">*</span> <span class="n">repeat</span>
    <span class="n">result</span> <span class="o">=</span> <span class="p">[[]]</span>
    <span class="k">for</span> <span class="n">pool</span> <span class="ow">in</span> <span class="n">pools</span><span class="p">:</span>
        <span class="n">result</span> <span class="o">=</span> <span class="p">[</span><span class="n">x</span><span class="o">+</span><span class="p">[</span><span class="n">y</span><span class="p">]</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">result</span> <span class="k">for</span> <span class="n">y</span> <span class="ow">in</span> <span class="n">pool</span><span class="p">]</span>
    <span class="k">for</span> <span class="n">prod</span> <span class="ow">in</span> <span class="n">result</span><span class="p">:</span>
        <span class="k">yield</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">prod</span><span class="p">)</span>
</pre></div>
</div>
</dd></dl>

<dl class="function">
<dt id="itertools.repeat">
<code class="descclassname">itertools.</code><code class="descname">repeat</code><span class="sig-paren">(</span><em>object</em><span class="optional">[</span>, <em>times</em><span class="optional">]</span><span class="sig-paren">)</span><a class="headerlink" href="#itertools.repeat" title="Permalink to this definition">¶</a></dt>
<dd><p>Make an iterator that returns <em>object</em> over and over again. Runs indefinitely
unless the <em>times</em> argument is specified. Used as argument to <a class="reference internal" href="functions.html#map" title="map"><code class="xref py py-func docutils literal"><span class="pre">map()</span></code></a> for
invariant parameters to the called function.  Also used with <a class="reference internal" href="functions.html#zip" title="zip"><code class="xref py py-func docutils literal"><span class="pre">zip()</span></code></a> to
create an invariant part of a tuple record.</p>
<p>Roughly equivalent to:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">repeat</span><span class="p">(</span><span class="nb">object</span><span class="p">,</span> <span class="n">times</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
    <span class="c1"># repeat(10, 3) --&gt; 10 10 10</span>
    <span class="k">if</span> <span class="n">times</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
        <span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
            <span class="k">yield</span> <span class="nb">object</span>
    <span class="k">else</span><span class="p">:</span>
        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">times</span><span class="p">):</span>
            <span class="k">yield</span> <span class="nb">object</span>
</pre></div>
</div>
<p>A common use for <em>repeat</em> is to supply a stream of constant values to <em>map</em>
or <em>zip</em>:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="nb">list</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">pow</span><span class="p">,</span> <span class="nb">range</span><span class="p">(</span><span class="mi">10</span><span class="p">),</span> <span class="n">repeat</span><span class="p">(</span><span class="mi">2</span><span class="p">)))</span>
<span class="go">[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]</span>
</pre></div>
</div>
</dd></dl>

<dl class="function">
<dt id="itertools.starmap">
<code class="descclassname">itertools.</code><code class="descname">starmap</code><span class="sig-paren">(</span><em>function</em>, <em>iterable</em><span class="sig-paren">)</span><a class="headerlink" href="#itertools.starmap" title="Permalink to this definition">¶</a></dt>
<dd><p>Make an iterator that computes the function using arguments obtained from
the iterable.  Used instead of <a class="reference internal" href="functions.html#map" title="map"><code class="xref py py-func docutils literal"><span class="pre">map()</span></code></a> when argument parameters are already
grouped in tuples from a single iterable (the data has been “pre-zipped”).  The
difference between <a class="reference internal" href="functions.html#map" title="map"><code class="xref py py-func docutils literal"><span class="pre">map()</span></code></a> and <a class="reference internal" href="#itertools.starmap" title="itertools.starmap"><code class="xref py py-func docutils literal"><span class="pre">starmap()</span></code></a> parallels the distinction
between <code class="docutils literal"><span class="pre">function(a,b)</span></code> and <code class="docutils literal"><span class="pre">function(*c)</span></code>. Roughly equivalent to:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">starmap</span><span class="p">(</span><span class="n">function</span><span class="p">,</span> <span class="n">iterable</span><span class="p">):</span>
    <span class="c1"># starmap(pow, [(2,5), (3,2), (10,3)]) --&gt; 32 9 1000</span>
    <span class="k">for</span> <span class="n">args</span> <span class="ow">in</span> <span class="n">iterable</span><span class="p">:</span>
        <span class="k">yield</span> <span class="n">function</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">)</span>
</pre></div>
</div>
</dd></dl>

<dl class="function">
<dt id="itertools.takewhile">
<code class="descclassname">itertools.</code><code class="descname">takewhile</code><span class="sig-paren">(</span><em>predicate</em>, <em>iterable</em><span class="sig-paren">)</span><a class="headerlink" href="#itertools.takewhile" title="Permalink to this definition">¶</a></dt>
<dd><p>Make an iterator that returns elements from the iterable as long as the
predicate is true.  Roughly equivalent to:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">takewhile</span><span class="p">(</span><span class="n">predicate</span><span class="p">,</span> <span class="n">iterable</span><span class="p">):</span>
    <span class="c1"># takewhile(lambda x: x&lt;5, [1,4,6,4,1]) --&gt; 1 4</span>
    <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">iterable</span><span class="p">:</span>
        <span class="k">if</span> <span class="n">predicate</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
            <span class="k">yield</span> <span class="n">x</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="k">break</span>
</pre></div>
</div>
</dd></dl>

<dl class="function">
<dt id="itertools.tee">
<code class="descclassname">itertools.</code><code class="descname">tee</code><span class="sig-paren">(</span><em>iterable</em>, <em>n=2</em><span class="sig-paren">)</span><a class="headerlink" href="#itertools.tee" title="Permalink to this definition">¶</a></dt>
<dd><p>Return <em>n</em> independent iterators from a single iterable.</p>
<p>The following Python code helps explain what <em>tee</em> does (although the actual
implementation is more complex and uses only a single underlying
<abbr title="first-in, first-out">FIFO</abbr> queue).</p>
<p>Roughly equivalent to:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">tee</span><span class="p">(</span><span class="n">iterable</span><span class="p">,</span> <span class="n">n</span><span class="o">=</span><span class="mi">2</span><span class="p">):</span>
    <span class="n">it</span> <span class="o">=</span> <span class="nb">iter</span><span class="p">(</span><span class="n">iterable</span><span class="p">)</span>
    <span class="n">deques</span> <span class="o">=</span> <span class="p">[</span><span class="n">collections</span><span class="o">.</span><span class="n">deque</span><span class="p">()</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">)]</span>
    <span class="k">def</span> <span class="nf">gen</span><span class="p">(</span><span class="n">mydeque</span><span class="p">):</span>
        <span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
            <span class="k">if</span> <span class="ow">not</span> <span class="n">mydeque</span><span class="p">:</span>             <span class="c1"># when the local deque is empty</span>
                <span class="k">try</span><span class="p">:</span>
                    <span class="n">newval</span> <span class="o">=</span> <span class="nb">next</span><span class="p">(</span><span class="n">it</span><span class="p">)</span>   <span class="c1"># fetch a new value and</span>
                <span class="k">except</span> <span class="ne">StopIteration</span><span class="p">:</span>
                    <span class="k">return</span>
                <span class="k">for</span> <span class="n">d</span> <span class="ow">in</span> <span class="n">deques</span><span class="p">:</span>        <span class="c1"># load it to all the deques</span>
                    <span class="n">d</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">newval</span><span class="p">)</span>
            <span class="k">yield</span> <span class="n">mydeque</span><span class="o">.</span><span class="n">popleft</span><span class="p">()</span>
    <span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">gen</span><span class="p">(</span><span class="n">d</span><span class="p">)</span> <span class="k">for</span> <span class="n">d</span> <span class="ow">in</span> <span class="n">deques</span><span class="p">)</span>
</pre></div>
</div>
<p>Once <a class="reference internal" href="#itertools.tee" title="itertools.tee"><code class="xref py py-func docutils literal"><span class="pre">tee()</span></code></a> has made a split, the original <em>iterable</em> should not be
used anywhere else; otherwise, the <em>iterable</em> could get advanced without
the tee objects being informed.</p>
<p>This itertool may require significant auxiliary storage (depending on how
much temporary data needs to be stored). In general, if one iterator uses
most or all of the data before another iterator starts, it is faster to use
<a class="reference internal" href="stdtypes.html#list" title="list"><code class="xref py py-func docutils literal"><span class="pre">list()</span></code></a> instead of <a class="reference internal" href="#itertools.tee" title="itertools.tee"><code class="xref py py-func docutils literal"><span class="pre">tee()</span></code></a>.</p>
</dd></dl>

<dl class="function">
<dt id="itertools.zip_longest">
<code class="descclassname">itertools.</code><code class="descname">zip_longest</code><span class="sig-paren">(</span><em>*iterables</em>, <em>fillvalue=None</em><span class="sig-paren">)</span><a class="headerlink" href="#itertools.zip_longest" title="Permalink to this definition">¶</a></dt>
<dd><p>Make an iterator that aggregates elements from each of the iterables. If the
iterables are of uneven length, missing values are filled-in with <em>fillvalue</em>.
Iteration continues until the longest iterable is exhausted.  Roughly equivalent to:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">ZipExhausted</span><span class="p">(</span><span class="ne">Exception</span><span class="p">):</span>
    <span class="k">pass</span>

<span class="k">def</span> <span class="nf">zip_longest</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwds</span><span class="p">):</span>
    <span class="c1"># zip_longest(&#39;ABCD&#39;, &#39;xy&#39;, fillvalue=&#39;-&#39;) --&gt; Ax By C- D-</span>
    <span class="n">fillvalue</span> <span class="o">=</span> <span class="n">kwds</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;fillvalue&#39;</span><span class="p">)</span>
    <span class="n">counter</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">args</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>
    <span class="k">def</span> <span class="nf">sentinel</span><span class="p">():</span>
        <span class="k">nonlocal</span> <span class="n">counter</span>
        <span class="k">if</span> <span class="ow">not</span> <span class="n">counter</span><span class="p">:</span>
            <span class="k">raise</span> <span class="n">ZipExhausted</span>
        <span class="n">counter</span> <span class="o">-=</span> <span class="mi">1</span>
        <span class="k">yield</span> <span class="n">fillvalue</span>
    <span class="n">fillers</span> <span class="o">=</span> <span class="n">repeat</span><span class="p">(</span><span class="n">fillvalue</span><span class="p">)</span>
    <span class="n">iterators</span> <span class="o">=</span> <span class="p">[</span><span class="n">chain</span><span class="p">(</span><span class="n">it</span><span class="p">,</span> <span class="n">sentinel</span><span class="p">(),</span> <span class="n">fillers</span><span class="p">)</span> <span class="k">for</span> <span class="n">it</span> <span class="ow">in</span> <span class="n">args</span><span class="p">]</span>
    <span class="k">try</span><span class="p">:</span>
        <span class="k">while</span> <span class="n">iterators</span><span class="p">:</span>
            <span class="k">yield</span> <span class="nb">tuple</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">next</span><span class="p">,</span> <span class="n">iterators</span><span class="p">))</span>
    <span class="k">except</span> <span class="n">ZipExhausted</span><span class="p">:</span>
        <span class="k">pass</span>
</pre></div>
</div>
<p>If one of the iterables is potentially infinite, then the <a class="reference internal" href="#itertools.zip_longest" title="itertools.zip_longest"><code class="xref py py-func docutils literal"><span class="pre">zip_longest()</span></code></a>
function should be wrapped with something that limits the number of calls
(for example <a class="reference internal" href="#itertools.islice" title="itertools.islice"><code class="xref py py-func docutils literal"><span class="pre">islice()</span></code></a> or <a class="reference internal" href="#itertools.takewhile" title="itertools.takewhile"><code class="xref py py-func docutils literal"><span class="pre">takewhile()</span></code></a>).  If not specified,
<em>fillvalue</em> defaults to <code class="docutils literal"><span class="pre">None</span></code>.</p>
</dd></dl>

</div>
<div class="section" id="itertools-recipes">
<span id="id1"></span><h2>10.1.2. Itertools Recipes<a class="headerlink" href="#itertools-recipes" title="Permalink to this headline">¶</a></h2>
<p>This section shows recipes for creating an extended toolset using the existing
itertools as building blocks.</p>
<p>The extended tools offer the same high performance as the underlying toolset.
The superior memory performance is kept by processing elements one at a time
rather than bringing the whole iterable into memory all at once. Code volume is
kept small by linking the tools together in a functional style which helps
eliminate temporary variables.  High speed is retained by preferring
“vectorized” building blocks over the use of for-loops and <a class="reference internal" href="../glossary.html#term-generator"><span class="xref std std-term">generator</span></a>s
which incur interpreter overhead.</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">take</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">iterable</span><span class="p">):</span>
    <span class="s2">&quot;Return first n items of the iterable as a list&quot;</span>
    <span class="k">return</span> <span class="nb">list</span><span class="p">(</span><span class="n">islice</span><span class="p">(</span><span class="n">iterable</span><span class="p">,</span> <span class="n">n</span><span class="p">))</span>

<span class="k">def</span> <span class="nf">tabulate</span><span class="p">(</span><span class="n">function</span><span class="p">,</span> <span class="n">start</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
    <span class="s2">&quot;Return function(0), function(1), ...&quot;</span>
    <span class="k">return</span> <span class="nb">map</span><span class="p">(</span><span class="n">function</span><span class="p">,</span> <span class="n">count</span><span class="p">(</span><span class="n">start</span><span class="p">))</span>

<span class="k">def</span> <span class="nf">tail</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">iterable</span><span class="p">):</span>
    <span class="s2">&quot;Return an iterator over the last n items&quot;</span>
    <span class="c1"># tail(3, &#39;ABCDEFG&#39;) --&gt; E F G</span>
    <span class="k">return</span> <span class="nb">iter</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">deque</span><span class="p">(</span><span class="n">iterable</span><span class="p">,</span> <span class="n">maxlen</span><span class="o">=</span><span class="n">n</span><span class="p">))</span>

<span class="k">def</span> <span class="nf">consume</span><span class="p">(</span><span class="n">iterator</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span>
    <span class="s2">&quot;Advance the iterator n-steps ahead. If n is none, consume entirely.&quot;</span>
    <span class="c1"># Use functions that consume iterators at C speed.</span>
    <span class="k">if</span> <span class="n">n</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
        <span class="c1"># feed the entire iterator into a zero-length deque</span>
        <span class="n">collections</span><span class="o">.</span><span class="n">deque</span><span class="p">(</span><span class="n">iterator</span><span class="p">,</span> <span class="n">maxlen</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
    <span class="k">else</span><span class="p">:</span>
        <span class="c1"># advance to the empty slice starting at position n</span>
        <span class="nb">next</span><span class="p">(</span><span class="n">islice</span><span class="p">(</span><span class="n">iterator</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">n</span><span class="p">),</span> <span class="kc">None</span><span class="p">)</span>

<span class="k">def</span> <span class="nf">nth</span><span class="p">(</span><span class="n">iterable</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">default</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
    <span class="s2">&quot;Returns the nth item or a default value&quot;</span>
    <span class="k">return</span> <span class="nb">next</span><span class="p">(</span><span class="n">islice</span><span class="p">(</span><span class="n">iterable</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="kc">None</span><span class="p">),</span> <span class="n">default</span><span class="p">)</span>

<span class="k">def</span> <span class="nf">all_equal</span><span class="p">(</span><span class="n">iterable</span><span class="p">):</span>
    <span class="s2">&quot;Returns True if all the elements are equal to each other&quot;</span>
    <span class="n">g</span> <span class="o">=</span> <span class="n">groupby</span><span class="p">(</span><span class="n">iterable</span><span class="p">)</span>
    <span class="k">return</span> <span class="nb">next</span><span class="p">(</span><span class="n">g</span><span class="p">,</span> <span class="kc">True</span><span class="p">)</span> <span class="ow">and</span> <span class="ow">not</span> <span class="nb">next</span><span class="p">(</span><span class="n">g</span><span class="p">,</span> <span class="kc">False</span><span class="p">)</span>

<span class="k">def</span> <span class="nf">quantify</span><span class="p">(</span><span class="n">iterable</span><span class="p">,</span> <span class="n">pred</span><span class="o">=</span><span class="nb">bool</span><span class="p">):</span>
    <span class="s2">&quot;Count how many times the predicate is true&quot;</span>
    <span class="k">return</span> <span class="nb">sum</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="n">pred</span><span class="p">,</span> <span class="n">iterable</span><span class="p">))</span>

<span class="k">def</span> <span class="nf">padnone</span><span class="p">(</span><span class="n">iterable</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;Returns the sequence elements and then returns None indefinitely.</span>

<span class="sd">    Useful for emulating the behavior of the built-in map() function.</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="k">return</span> <span class="n">chain</span><span class="p">(</span><span class="n">iterable</span><span class="p">,</span> <span class="n">repeat</span><span class="p">(</span><span class="kc">None</span><span class="p">))</span>

<span class="k">def</span> <span class="nf">ncycles</span><span class="p">(</span><span class="n">iterable</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span>
    <span class="s2">&quot;Returns the sequence elements n times&quot;</span>
    <span class="k">return</span> <span class="n">chain</span><span class="o">.</span><span class="n">from_iterable</span><span class="p">(</span><span class="n">repeat</span><span class="p">(</span><span class="nb">tuple</span><span class="p">(</span><span class="n">iterable</span><span class="p">),</span> <span class="n">n</span><span class="p">))</span>

<span class="k">def</span> <span class="nf">dotproduct</span><span class="p">(</span><span class="n">vec1</span><span class="p">,</span> <span class="n">vec2</span><span class="p">):</span>
    <span class="k">return</span> <span class="nb">sum</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="n">operator</span><span class="o">.</span><span class="n">mul</span><span class="p">,</span> <span class="n">vec1</span><span class="p">,</span> <span class="n">vec2</span><span class="p">))</span>

<span class="k">def</span> <span class="nf">flatten</span><span class="p">(</span><span class="n">listOfLists</span><span class="p">):</span>
    <span class="s2">&quot;Flatten one level of nesting&quot;</span>
    <span class="k">return</span> <span class="n">chain</span><span class="o">.</span><span class="n">from_iterable</span><span class="p">(</span><span class="n">listOfLists</span><span class="p">)</span>

<span class="k">def</span> <span class="nf">repeatfunc</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="n">times</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;Repeat calls to func with specified arguments.</span>

<span class="sd">    Example:  repeatfunc(random.random)</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="k">if</span> <span class="n">times</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
        <span class="k">return</span> <span class="n">starmap</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="n">repeat</span><span class="p">(</span><span class="n">args</span><span class="p">))</span>
    <span class="k">return</span> <span class="n">starmap</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="n">repeat</span><span class="p">(</span><span class="n">args</span><span class="p">,</span> <span class="n">times</span><span class="p">))</span>

<span class="k">def</span> <span class="nf">pairwise</span><span class="p">(</span><span class="n">iterable</span><span class="p">):</span>
    <span class="s2">&quot;s -&gt; (s0,s1), (s1,s2), (s2, s3), ...&quot;</span>
    <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="o">=</span> <span class="n">tee</span><span class="p">(</span><span class="n">iterable</span><span class="p">)</span>
    <span class="nb">next</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="kc">None</span><span class="p">)</span>
    <span class="k">return</span> <span class="nb">zip</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>

<span class="k">def</span> <span class="nf">grouper</span><span class="p">(</span><span class="n">iterable</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">fillvalue</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
    <span class="s2">&quot;Collect data into fixed-length chunks or blocks&quot;</span>
    <span class="c1"># grouper(&#39;ABCDEFG&#39;, 3, &#39;x&#39;) --&gt; ABC DEF Gxx&quot;</span>
    <span class="n">args</span> <span class="o">=</span> <span class="p">[</span><span class="nb">iter</span><span class="p">(</span><span class="n">iterable</span><span class="p">)]</span> <span class="o">*</span> <span class="n">n</span>
    <span class="k">return</span> <span class="n">zip_longest</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="n">fillvalue</span><span class="o">=</span><span class="n">fillvalue</span><span class="p">)</span>

<span class="k">def</span> <span class="nf">roundrobin</span><span class="p">(</span><span class="o">*</span><span class="n">iterables</span><span class="p">):</span>
    <span class="s2">&quot;roundrobin(&#39;ABC&#39;, &#39;D&#39;, &#39;EF&#39;) --&gt; A D E B F C&quot;</span>
    <span class="c1"># Recipe credited to George Sakkis</span>
    <span class="n">pending</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">iterables</span><span class="p">)</span>
    <span class="n">nexts</span> <span class="o">=</span> <span class="n">cycle</span><span class="p">(</span><span class="nb">iter</span><span class="p">(</span><span class="n">it</span><span class="p">)</span><span class="o">.</span><span class="fm">__next__</span> <span class="k">for</span> <span class="n">it</span> <span class="ow">in</span> <span class="n">iterables</span><span class="p">)</span>
    <span class="k">while</span> <span class="n">pending</span><span class="p">:</span>
        <span class="k">try</span><span class="p">:</span>
            <span class="k">for</span> <span class="nb">next</span> <span class="ow">in</span> <span class="n">nexts</span><span class="p">:</span>
                <span class="k">yield</span> <span class="nb">next</span><span class="p">()</span>
        <span class="k">except</span> <span class="ne">StopIteration</span><span class="p">:</span>
            <span class="n">pending</span> <span class="o">-=</span> <span class="mi">1</span>
            <span class="n">nexts</span> <span class="o">=</span> <span class="n">cycle</span><span class="p">(</span><span class="n">islice</span><span class="p">(</span><span class="n">nexts</span><span class="p">,</span> <span class="n">pending</span><span class="p">))</span>

<span class="k">def</span> <span class="nf">partition</span><span class="p">(</span><span class="n">pred</span><span class="p">,</span> <span class="n">iterable</span><span class="p">):</span>
    <span class="s1">&#39;Use a predicate to partition entries into false entries and true entries&#39;</span>
    <span class="c1"># partition(is_odd, range(10)) --&gt; 0 2 4 6 8   and  1 3 5 7 9</span>
    <span class="n">t1</span><span class="p">,</span> <span class="n">t2</span> <span class="o">=</span> <span class="n">tee</span><span class="p">(</span><span class="n">iterable</span><span class="p">)</span>
    <span class="k">return</span> <span class="n">filterfalse</span><span class="p">(</span><span class="n">pred</span><span class="p">,</span> <span class="n">t1</span><span class="p">),</span> <span class="nb">filter</span><span class="p">(</span><span class="n">pred</span><span class="p">,</span> <span class="n">t2</span><span class="p">)</span>

<span class="k">def</span> <span class="nf">powerset</span><span class="p">(</span><span class="n">iterable</span><span class="p">):</span>
    <span class="s2">&quot;powerset([1,2,3]) --&gt; () (1,) (2,) (3,) (1,2) (1,3) (2,3) (1,2,3)&quot;</span>
    <span class="n">s</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">iterable</span><span class="p">)</span>
    <span class="k">return</span> <span class="n">chain</span><span class="o">.</span><span class="n">from_iterable</span><span class="p">(</span><span class="n">combinations</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">r</span><span class="p">)</span> <span class="k">for</span> <span class="n">r</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">s</span><span class="p">)</span><span class="o">+</span><span class="mi">1</span><span class="p">))</span>

<span class="k">def</span> <span class="nf">unique_everseen</span><span class="p">(</span><span class="n">iterable</span><span class="p">,</span> <span class="n">key</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
    <span class="s2">&quot;List unique elements, preserving order. Remember all elements ever seen.&quot;</span>
    <span class="c1"># unique_everseen(&#39;AAAABBBCCDAABBB&#39;) --&gt; A B C D</span>
    <span class="c1"># unique_everseen(&#39;ABBCcAD&#39;, str.lower) --&gt; A B C D</span>
    <span class="n">seen</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
    <span class="n">seen_add</span> <span class="o">=</span> <span class="n">seen</span><span class="o">.</span><span class="n">add</span>
    <span class="k">if</span> <span class="n">key</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
        <span class="k">for</span> <span class="n">element</span> <span class="ow">in</span> <span class="n">filterfalse</span><span class="p">(</span><span class="n">seen</span><span class="o">.</span><span class="fm">__contains__</span><span class="p">,</span> <span class="n">iterable</span><span class="p">):</span>
            <span class="n">seen_add</span><span class="p">(</span><span class="n">element</span><span class="p">)</span>
            <span class="k">yield</span> <span class="n">element</span>
    <span class="k">else</span><span class="p">:</span>
        <span class="k">for</span> <span class="n">element</span> <span class="ow">in</span> <span class="n">iterable</span><span class="p">:</span>
            <span class="n">k</span> <span class="o">=</span> <span class="n">key</span><span class="p">(</span><span class="n">element</span><span class="p">)</span>
            <span class="k">if</span> <span class="n">k</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">seen</span><span class="p">:</span>
                <span class="n">seen_add</span><span class="p">(</span><span class="n">k</span><span class="p">)</span>
                <span class="k">yield</span> <span class="n">element</span>

<span class="k">def</span> <span class="nf">unique_justseen</span><span class="p">(</span><span class="n">iterable</span><span class="p">,</span> <span class="n">key</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
    <span class="s2">&quot;List unique elements, preserving order. Remember only the element just seen.&quot;</span>
    <span class="c1"># unique_justseen(&#39;AAAABBBCCDAABBB&#39;) --&gt; A B C D A B</span>
    <span class="c1"># unique_justseen(&#39;ABBCcAD&#39;, str.lower) --&gt; A B C A D</span>
    <span class="k">return</span> <span class="nb">map</span><span class="p">(</span><span class="nb">next</span><span class="p">,</span> <span class="nb">map</span><span class="p">(</span><span class="n">itemgetter</span><span class="p">(</span><span class="mi">1</span><span class="p">),</span> <span class="n">groupby</span><span class="p">(</span><span class="n">iterable</span><span class="p">,</span> <span class="n">key</span><span class="p">)))</span>

<span class="k">def</span> <span class="nf">iter_except</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="n">exception</span><span class="p">,</span> <span class="n">first</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot; Call a function repeatedly until an exception is raised.</span>

<span class="sd">    Converts a call-until-exception interface to an iterator interface.</span>
<span class="sd">    Like builtins.iter(func, sentinel) but uses an exception instead</span>
<span class="sd">    of a sentinel to end the loop.</span>

<span class="sd">    Examples:</span>
<span class="sd">        iter_except(functools.partial(heappop, h), IndexError)   # priority queue iterator</span>
<span class="sd">        iter_except(d.popitem, KeyError)                         # non-blocking dict iterator</span>
<span class="sd">        iter_except(d.popleft, IndexError)                       # non-blocking deque iterator</span>
<span class="sd">        iter_except(q.get_nowait, Queue.Empty)                   # loop over a producer Queue</span>
<span class="sd">        iter_except(s.pop, KeyError)                             # non-blocking set iterator</span>

<span class="sd">    &quot;&quot;&quot;</span>
    <span class="k">try</span><span class="p">:</span>
        <span class="k">if</span> <span class="n">first</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
            <span class="k">yield</span> <span class="n">first</span><span class="p">()</span>            <span class="c1"># For database APIs needing an initial cast to db.first()</span>
        <span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
            <span class="k">yield</span> <span class="n">func</span><span class="p">()</span>
    <span class="k">except</span> <span class="n">exception</span><span class="p">:</span>
        <span class="k">pass</span>

<span class="k">def</span> <span class="nf">first_true</span><span class="p">(</span><span class="n">iterable</span><span class="p">,</span> <span class="n">default</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">pred</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;Returns the first true value in the iterable.</span>

<span class="sd">    If no true value is found, returns *default*</span>

<span class="sd">    If *pred* is not None, returns the first item</span>
<span class="sd">    for which pred(item) is true.</span>

<span class="sd">    &quot;&quot;&quot;</span>
    <span class="c1"># first_true([a,b,c], x) --&gt; a or b or c or x</span>
    <span class="c1"># first_true([a,b], x, f) --&gt; a if f(a) else b if f(b) else x</span>
    <span class="k">return</span> <span class="nb">next</span><span class="p">(</span><span class="nb">filter</span><span class="p">(</span><span class="n">pred</span><span class="p">,</span> <span class="n">iterable</span><span class="p">),</span> <span class="n">default</span><span class="p">)</span>

<span class="k">def</span> <span class="nf">random_product</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="n">repeat</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
    <span class="s2">&quot;Random selection from itertools.product(*args, **kwds)&quot;</span>
    <span class="n">pools</span> <span class="o">=</span> <span class="p">[</span><span class="nb">tuple</span><span class="p">(</span><span class="n">pool</span><span class="p">)</span> <span class="k">for</span> <span class="n">pool</span> <span class="ow">in</span> <span class="n">args</span><span class="p">]</span> <span class="o">*</span> <span class="n">repeat</span>
    <span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">choice</span><span class="p">(</span><span class="n">pool</span><span class="p">)</span> <span class="k">for</span> <span class="n">pool</span> <span class="ow">in</span> <span class="n">pools</span><span class="p">)</span>

<span class="k">def</span> <span class="nf">random_permutation</span><span class="p">(</span><span class="n">iterable</span><span class="p">,</span> <span class="n">r</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
    <span class="s2">&quot;Random selection from itertools.permutations(iterable, r)&quot;</span>
    <span class="n">pool</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">iterable</span><span class="p">)</span>
    <span class="n">r</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">pool</span><span class="p">)</span> <span class="k">if</span> <span class="n">r</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="n">r</span>
    <span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">sample</span><span class="p">(</span><span class="n">pool</span><span class="p">,</span> <span class="n">r</span><span class="p">))</span>

<span class="k">def</span> <span class="nf">random_combination</span><span class="p">(</span><span class="n">iterable</span><span class="p">,</span> <span class="n">r</span><span class="p">):</span>
    <span class="s2">&quot;Random selection from itertools.combinations(iterable, r)&quot;</span>
    <span class="n">pool</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">iterable</span><span class="p">)</span>
    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">pool</span><span class="p">)</span>
    <span class="n">indices</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">sample</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">),</span> <span class="n">r</span><span class="p">))</span>
    <span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">pool</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">indices</span><span class="p">)</span>

<span class="k">def</span> <span class="nf">random_combination_with_replacement</span><span class="p">(</span><span class="n">iterable</span><span class="p">,</span> <span class="n">r</span><span class="p">):</span>
    <span class="s2">&quot;Random selection from itertools.combinations_with_replacement(iterable, r)&quot;</span>
    <span class="n">pool</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">iterable</span><span class="p">)</span>
    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">pool</span><span class="p">)</span>
    <span class="n">indices</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">randrange</span><span class="p">(</span><span class="n">n</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">r</span><span class="p">))</span>
    <span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">pool</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">indices</span><span class="p">)</span>
</pre></div>
</div>
<p>Note, many of the above recipes can be optimized by replacing global lookups
with local variables defined as default values.  For example, the
<em>dotproduct</em> recipe can be written as:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">dotproduct</span><span class="p">(</span><span class="n">vec1</span><span class="p">,</span> <span class="n">vec2</span><span class="p">,</span> <span class="nb">sum</span><span class="o">=</span><span class="nb">sum</span><span class="p">,</span> <span class="nb">map</span><span class="o">=</span><span class="nb">map</span><span class="p">,</span> <span class="n">mul</span><span class="o">=</span><span class="n">operator</span><span class="o">.</span><span class="n">mul</span><span class="p">):</span>
    <span class="k">return</span> <span class="nb">sum</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="n">mul</span><span class="p">,</span> <span class="n">vec1</span><span class="p">,</span> <span class="n">vec2</span><span class="p">))</span>
</pre></div>
</div>
</div>
</div>


          </div>
        </div>
      </div>
      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
        <div class="sphinxsidebarwrapper">
  <h3><a href="../contents.html">Table Of Contents</a></h3>
  <ul>
<li><a class="reference internal" href="#">10.1. <code class="docutils literal"><span class="pre">itertools</span></code> — Functions creating iterators for efficient looping</a><ul>
<li><a class="reference internal" href="#itertool-functions">10.1.1. Itertool functions</a></li>
<li><a class="reference internal" href="#itertools-recipes">10.1.2. Itertools Recipes</a></li>
</ul>
</li>
</ul>

  <h4>Previous topic</h4>
  <p class="topless"><a href="functional.html"
                        title="previous chapter">10. Functional Programming Modules</a></p>
  <h4>Next topic</h4>
  <p class="topless"><a href="functools.html"
                        title="next chapter">10.2. <code class="docutils literal"><span class="pre">functools</span></code> — Higher-order functions and operations on callable objects</a></p>
  <div role="note" aria-label="source link">
    <h3>This Page</h3>
    <ul class="this-page-menu">
      <li><a href="../bugs.html">Report a Bug</a></li>
      <li>
        <a href="https://github.com/python/cpython/blob/3.6/Doc/library/itertools.rst"
            rel="nofollow">Show Source
        </a>
      </li>
    </ul>
  </div>
        </div>
      </div>
      <div class="clearer"></div>
    </div>  
    <div class="related" role="navigation" aria-label="related navigation">
      <h3>Navigation</h3>
      <ul>
        <li class="right" style="margin-right: 10px">
          <a href="../genindex.html" title="General Index"
             >index</a></li>
        <li class="right" >
          <a href="../py-modindex.html" title="Python Module Index"
             >modules</a> |</li>
        <li class="right" >
          <a href="functools.html" title="10.2. functools — Higher-order functions and operations on callable objects"
             >next</a> |</li>
        <li class="right" >
          <a href="functional.html" title="10. Functional Programming Modules"
             >previous</a> |</li>
        <li><img src="../_static/py.png" alt=""
                 style="vertical-align: middle; margin-top: -1px"/></li>
        <li><a href="https://www.python.org/">Python</a> &#187;</li>
        <li>
          <span class="language_switcher_placeholder">en</span>
          <span class="version_switcher_placeholder">3.6.3</span>
          <a href="../index.html">Documentation </a> &#187;
        </li>

          <li class="nav-item nav-item-1"><a href="index.html" >The Python Standard Library</a> &#187;</li>
          <li class="nav-item nav-item-2"><a href="functional.html" >10. Functional Programming Modules</a> &#187;</li>
    <li class="right">
        

    <div class="inline-search" style="display: none" role="search">
        <form class="inline-search" action="../search.html" method="get">
          <input placeholder="Quick search" type="text" name="q" />
          <input type="submit" value="Go" />
          <input type="hidden" name="check_keywords" value="yes" />
          <input type="hidden" name="area" value="default" />
        </form>
    </div>
    <script type="text/javascript">$('.inline-search').show(0);</script>
         |
    </li>

      </ul>
    </div>  
    <div class="footer">
    &copy; <a href="../copyright.html">Copyright</a> 2001-2017, Python Software Foundation.
    <br />
    The Python Software Foundation is a non-profit corporation.
    <a href="https://www.python.org/psf/donations/">Please donate.</a>
    <br />
    Last updated on Oct 14, 2017.
    <a href="../bugs.html">Found a bug</a>?
    <br />
    Created using <a href="http://sphinx.pocoo.org/">Sphinx</a> 1.6.4.
    </div>

  </body>
</html>